Problem: Simplify the following expression: $\sqrt{24}-\sqrt{96}+\sqrt{54}$
Solution: First, try to factor any perfect squares out of the radicals. $= \sqrt{24}-\sqrt{96}+\sqrt{54}$ $= \sqrt{4 \cdot 6}-\sqrt{16 \cdot 6}+\sqrt{9 \cdot 6}$ Separate the radicals and simplify. $= \sqrt{4} \cdot \sqrt{6}-\sqrt{16} \cdot \sqrt{6}+\sqrt{9} \cdot \sqrt{6}$ $= 2\sqrt{6}-4\sqrt{6}+3\sqrt{6}$ Finally, simplify by combining the terms. $= ( 2 - 4 + 3 )\sqrt{6} = \sqrt{6}$